Low-order, P-stable, two-step methods for use with lax accuracies

摘要

A semi-implicit family of two-step methods is considered for the numerical solution of y ''=f(x,y). These methods are hybrid and waste two stages (function evaluations) per step in order to attain fourth algebraic order while other methods of this type need three stages per step. Exploiting this improvement, we derive a particular method and conclude with a series of numerical tests on stiff periodic problems that illustrate its efficiency.